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Neuronal firing activities have attracted a lot of attention since a large population of spatiotemporal patterns in the brain is the basis for adaptive behavior and can also reveal the signs for various neurological disorders including…
The pattern dynamics of the one-way coupled logistic lattice which can serve as a phenomenological model for open flow is investigated and shown to be extremely rich. For medium and large coupling strengths, we find spatially periodic,…
Designing chaotic maps with complex dynamics is a challenging topic. This paper introduces the nonlinear chaotic processing (NCP) model, which contains six basic nonlinear operations. Each operation is a general framework that can use…
This paper presents an application of partial contraction analysis to the study of global synchronization in discrete chaotic systems. Explicit sufficient conditions on the coupling strength of networks of discrete oscillators are derived.…
Piecewise smooth systems are intensively studied today in many application areas, such as economics, finance, engineering, biology, and ecology. In this work, we consider a class of one-dimensional piecewise linear discontinuous maps with a…
Collective chaos is shown to emerge, via a period-doubling cascade, from quasiperiodic partial synchronization in a population of identical inhibitory neurons with delayed global coupling. This system is thoroughly investigated by means of…
Non-reciprocal interactions are a defining feature of many complex systems, biological, ecological, and technological, often pushing them far from equilibrium and enabling rich dynamical responses. These asymmetries can arise at multiple…
A naive model of many networked logistic maps with an excitation type coupling [Neural Networks, vol. 20, 102--108 (2007)], which is an extension of other low dimensional models, has been recently proposed to mimic the waking-sleeping…
The aim of this paper is to rigorously study dynamics of Heterogeneously Coupled Maps (HCM). Such systems are determined by a network with heterogeneous degrees. Some nodes, called hubs, are very well connected while most nodes interact…
Cross-correlations in the activity in neural networks are commonly used to characterize their dynamical states and their anatomical and functional organizations. Yet, how these latter network features affect the spatiotemporal structure of…
A model of the columnar functional organization of neocortical association areas is studied. The neuronal network is composed of many Hebbian autoassociators, or modules, each of which interacts with a relatively small number of the others.…
We examine the dynamical properties of a single-layer convolutional recurrent network with a smooth sigmoidal activation function, for small values of the inputs and when the convolution kernel is unitary, so all eigenvalues lie exactly at…
Artificial neural networks typically have a fixed, non-linear activation function at each neuron. We have designed a novel form of piecewise linear activation function that is learned independently for each neuron using gradient descent.…
The neuronal networks in the mammals cortex are characterized by the coexistence of hierarchy, modularity, short and long range interactions, spatial correlations, and topographical connections. Particularly interesting, the latter type of…
Recurrent Neural Network models have elucidated the interplay between structure and dynamics in biological neural networks, particularly the emergence of irregular and rhythmic activities in cortex. However, most studies have focused on…
We propose a hierarchically modular, dynamical neural network model whose architecture minimizes a specifically designed energy function and defines its temporal characteristics. The model has an internal and an external space that are…
Complex diseases can be modeled as damage to intracellular networks that results in abnormal cell behaviors. Network-based dynamic models such as Boolean models have been employed to model a variety of biological systems including those…
The advances in understanding complex networks have generated increasing interest in dynamical processes occurring on them. Pattern formation in activator-inhibitor systems has been studied in networks, revealing differences from the…
A great variety of systems in nature, society and technology -- from the web of sexual contacts to the Internet, from the nervous system to power grids -- can be modeled as graphs of vertices coupled by edges. The network structure,…
Neural network models in neuroscience allow one to study how the connections between neurons shape the activity of neural circuits in the brain. In this chapter, we study Combinatorial Threshold-Linear Networks (CTLNs) in order to…